Simplify: -4 1/5 - (-13 1/10)

13 2/5 - 4 1/5 = ?

13 2/5 - 4 1/5 = 9 1/5

To simplify the expression -4 1/5 - (-13 1/10), we can follow these steps:

Step 1: Convert the mixed numbers into improper fractions.
-4 1/5 becomes -(4 * 5 + 1)/5 = -21/5
-13 1/10 becomes -(13 * 10 + 1)/10 = -131/10

Step 2: Apply the rule for subtracting fractions.
To subtract fractions, we need to find a common denominator. In this case, the common denominator is 10.

Step 3: Subtract the fractions.
So, -21/5 - (-131/10) becomes:
(-21 * 2)/(5 * 2) - (-131 * 1)/(10 * 1) =
(-42/10) - (-131/10) =
-42/10 + 131/10

Step 4: Simplify the resulting fraction.
To add fractions, we add the numerators and keep the denominator the same. Hence, -42/10 + 131/10 equals (131 - 42)/10 = 89/10.

Therefore, -4 1/5 - (-13 1/10) simplifies to 89/10.